Sinn Fein president Gerry Adams has described his groundbreaking first meeting with the head of Northern Ireland's police force as "useful".
Gerry Adams met the police chief for the first time
The prime minister also attended the discussions between Mr Adams and Hugh Orde in Downing Street.
Mr Adams said that he had agreed to meet Mr Orde on the "hugely important" issue of the "demilitarisation of republican heartlands".
Mr Orde said the meeting was "very significant" and a "step forward".
DEMILITARISATION - THE FACTS
On 1 September 1994, there were 106 army bases in Northern Ireland.
By 29 November 2004, there were 43 bases, including 8 hilltop watchtowers.
63 bases have been demolished or vacated.
There are currently 11,000 soldiers based in Northern Ireland.
The plan is to reduce the Army presence to 5,000 soldiers and 14 bases in the next 18 months.
The meeting came as DUP leader Ian Paisley met the head of the decommissioning body to discuss any possible IRA disarmament.
The moves form part of intense talks aimed at reviving devolved government in Northern Ireland.
Its political institutions have been suspended since October 2002 amid claims of IRA intelligence-gathering at the Northern Ireland Office.
Leaving the meeting on Monday, Mr Paisley said negotiations remained at a "very delicate stage".
He said: "If this decommissioning problem can be solved, then we are on our way. But it is not solved at the present time."
Mr Paisley said he will meet Mr Blair in Downing Street on Tuesday.
"There are a host of things that need to be settled - we have to wait and see
what is going to happen," he said.
The British and Irish Governments had said they wanted Sinn Fein and the DUP to have decided by Tuesday whether to sign up to a new power-sharing deal.
Mr Blair said the talks were at a "intensive stage" and he did not want to raise hopes.
"I think probably the best thing is for me to say very little - so many times before, hopes have been raised and then dashed that I'm almost fearful of raising them," he said.
"It's obvious that people would like to get a deal done - whether that is possible or not, the next few days will tell us."
The Sinn Fein president's meeting with Mr Orde signalled a significant departure in his party's policy.
Mr Paisley said negotiations were at a delicate stage
Mr Adams said the discussions focused solely on demilitarisation, which he said was a vital part of the Good Friday Agreement.
The talks included issues such as scaling back security fortifications and cutting back on the Army's presence.
Mr Adams said: "We had a meeting on the issue of demilitarisation.
"The British prime minister had told us a number of things, that this was an operational matter for Hugh Orde and that's why we met in the format we did.
"And we did some other meetings around other issues. I think it was a useful
Mr Orde said that the meeting had been "constructive".
He said: "We discussed security, normalisation and policing.
"The fact that the meeting happened is very significant. It is the first time I have met Mr Adams and it was an opportunity to explain about policing and how we have moved on."
He said the aim was to provide an "ordinary" police service to people "across the divide".
Meanwhile, SDLP policing spokesman Alex Attwood said that he believed there could be significant demilitarisation within a short time.
He said: "I have no doubt that people can expect radical thinking on the time-frame for normalisation."
Early movement on the removal of watchtowers and the restoration of normal security arrangements could be completed in less than 18 months, he said.
Speaking after a party delegation met with the Secretary of State on Monday, SDLP leader Mark Durkan said its "main, underlying concern is securing an end to Direct Rule, suspension and drift".